Session Cc - General Instabilities.
ORAL session, Sunday, November 23
303, Moscone Center
Using a nonequilibrium, nonlinear critical layer, we consider the nonlinear evolution of a two-dimensional disturbance to a \tanh^3y mixing layer. The analysis is inviscid and incompressible. The distiguishing feature of this flow is that the first two derivatives of the base velocity both vanish at the critical layer, and as a result of this, the singularities at the critical layer are far worse than those normally encountered in nonlinear critical layer theory. Further, this flow has three neutral modes, each of which is singular at the critical layer and none of which appears to be a stability boundary. As a consequence of this, the evolution of the disturbance is governed by a set of equations which are more nonlinear than those derived by Goldstein amp; Leib (1988) for the more usual \tanh y mixing layer. These equations consist of a set of coupled nonlinear PDE's together with jump conditions across the critical layer.